2000/06/05 by J. H. Samson, J H Samson
Chemistry · Mathematics · Physics and Astronomy · #Advanced NMR Techniques and Applications #Centroid #Coherent states #Combinatorics #Diagonal #Gaussian #Geometry #Hamiltonian (control theory) #Mathematical analysis #Mathematical physics #Mathematics #Path integral formulation #Physics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Wigner distribution function #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/0305-4470/33/29/306
12 pages, 2 figures, to appear J Phys A. Requires IOP style files
arxiv created 2000/06/05 · openalex publication_date 2000/07/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We consider a set of operators = ( 1 ,..., N ) with diagonal representatives P ( n ) in the space of generalized coherent states | n ⟩: = ∫dµ( n ) P ( n )| n ⟩⟨ n |. We regularize the coherent-state path integral as a limit of a sequence of averages ⟨ ⟩ L over polygonal paths with L vertices n 1,..., L . The distribution of the path centroid = (1/ L )∑ l = 1 L P ( n l ) tends to the Wigner function W ( x ), the joint distribution for the operators: W ( x ) = lim L →∞ ⟨δ N ( x - )⟩ L . This result is proved in the case where the Hamiltonian commutes with . The Wigner function is non-positive if the dominant paths with path centroid in a certain region have Berry phases close to odd multiples of π. For finite L the path centroid distribution is a Wigner function convolved with a Gaussian of variance inversely proportional to L . The results are illustrated by numerical calculations of the spin Wigner function from SU (2) coherent states. The relevance to the quantum Monte Carlo sign problem is also discussed.